You'll need a slice of bread, the center of which you've pinched a hole in; some butter, and extra virgin olive oil (MUST be extra virgin). Be more generous with the oil than the butter.
Heat the oil and butter at medium heat in a non-stick fry pan. Olive oil burns very easily--the butter keeps it from doing that. I don't understand all of the science, but it works.
Crack the egg so that it sits nicely in the "hole" in the bread. Let it fry for a few minutes.
Flip it over and let it fry on the other side.
It's really delicious--the bread is all toasty-crunchy, and the yolk of the egg is still soft. It's even better if you use large slices of Italian bread. Enjoy!